TMUA Preparation Programme

This programme is fifteen 90-minute tutorials that build the mathematical knowledge, reasoning skills and exam technique required for the Test of Mathematics for University Admission. It focuses not just on reaching the right answer, but on finding efficient, reliable and well-reasoned approaches under time pressure — recognising common question structures, spotting useful simplifications and selecting the right method with confidence.

Organised by topic and question type first, then mixed questions and timed mock exams
The most recent official papers are reserved for realistic timed mocks

What makes our approach different

Efficient methods under pressure

We focus on the key idea behind each problem, avoiding unnecessary calculation and building fast, reliable methods for the clock.

Reasoning, not just answers

Students explain their reasoning, compare alternative approaches and learn why particular methods succeed or fail.

Homework review & error logs

Recurring mistakes are reviewed every lesson, and each student keeps an error log that turns weaknesses into marks.

Growing independence

As the programme progresses the level of guidance decreases, building confident, independent problem-solvers ready for exam day.

Curriculum

A 15-tutorial plan. Sessions 1–9 build the Paper 1 topics (applying mathematical knowledge); sessions 10–15 develop the Paper 2 logic and proof skills (mathematical reasoning).

Session	Focus
1	Algebra & functions I
2	Algebra & functions II
3	Sequences & series
4	Coordinate geometry
5	Trigonometry
6	Exponentials & logarithms
7	Differentiation
8	Integration
9	Probability & statistics
10	Necessary vs sufficient conditions
11	Quantifier negation
12	The four directions of implication
13	Disproof by counterexample
14	Proof techniques
15	Spotting errors in proofs

Before the first session, students review the given prerequisite concepts.

How the course works

Course materials

Official TMUA specimen and past papers
Selected multiple-choice questions from MAT past papers
Timed question sets and full mock examinations
Solution notes, error logs and progress-review materials

A typical 90-minute lesson

Review of homework and recurring mistakes
The lesson’s main topic or strategy, explained clearly
Tutor-led examples of efficient methods
Guided and independent TMUA problem-solving
Short timed exercises, then a summary and homework brief

What students do between lessons

Complete the assigned preparation and homework before each lesson
Submit work in advance where requested
Keep an error log: the question, the reason for the mistake, the correct method and how to avoid it next time

TMUA